Stability of fractional order of time nonlinear fractional diffusion equation with Riemann–Liouville derivative
Le Dinh Long, Ho Duy Binh, Devendra Kumar, Nguyen Hoang Luc, Nguyen Huu Can
Abstract
In this paper, we investigate an equation of nonlinear fractional diffusion with the derivative of Riemann–Liouville. Firstly, we determine the global existence and uniqueness of the mild solution. Next, under some assumptions on the input data, we discuss continuity with regard to the fractional derivative order for the time. Our key idea is to combine the theories Mittag–Leffler functions and Banach fixed‐point theorem. Finally, we present some examples to test the proposed theory.
Topics & Concepts
MathematicsFractional calculusUniquenessDerivative (finance)Nonlinear systemFixed-point theoremOrder (exchange)Stability (learning theory)Mathematical analysisApplied mathematicsBanach fixed-point theoremRiemann hypothesisPure mathematicsFinancial economicsPhysicsFinanceComputer scienceQuantum mechanicsMachine learningEconomicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods